Problem: Solve for $x$ and $y$ using substitution. ${x-6y = -2}$ ${x = -2y-10}$
Answer: Since $x$ has already been solved for, substitute $-2y-10$ for $x$ in the first equation. ${(-2y-10)}{- 6y = -2}$ Simplify and solve for $y$ $-2y-10 - 6y = -2$ $-8y-10 = -2$ $-8y-10{+10} = -2{+10}$ $-8y = 8$ $\dfrac{-8y}{{-8}} = \dfrac{8}{{-8}}$ ${y = -1}$ Now that you know ${y = -1}$ , plug it back into $\thinspace {x = -2y-10}\thinspace$ to find $x$ ${x = -2}{(-1)}{ - 10}$ $x = 2 - 10$ ${x = -8}$ You can also plug ${y = -1}$ into $\thinspace {x-6y = -2}\thinspace$ and get the same answer for $x$ : ${x - 6}{(-1)}{= -2}$ ${x = -8}$